Algebra Examples

${(- 27)}^{- \frac{2}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(- 27)}^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

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Rewrite $- 27$ as ${(- 3)}^{3}$ .

$\frac{1}{{({(- 3)}^{3})}^{\frac{2}{3}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{{(- 3)}^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{1}{{(- 3)}^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{1}{{(- 3)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\frac{1}{9}$